Techniques for extreme rainfall and flood runoff estimation

The research of the group focused on real-time forecasting and simulation for design purposes, frequency estimation of peak flows and flood inundation, and the understanding of runoff generation processes. In most of the catchments studied not only rainfall but also snow is important. A central aspect is an effort to estimate uncertainty in the predictions. The following sections describe the topics studied in more detail.

Assimilating satellite-derived snow-covered area (SCA) in hydrological models

A major cause of flooding in Norway is the combination of intense snowmelt and precipitation. To be able to forecast these flooding events, reliable forecasts of precipitation and temperature are needed, along with a good estimate of the snow reservoir and its coverage in the catchment at the time of the forecast. Modelling the SCA correctly is considered a prerequisite for the applied rainfall-runoff model to capture the dynamics of the snowmelt-induced spring flood, and through this study, an analytical link between SCA and the parameters of the spatial distribution of snow water equivalent (SWE) has been developed.

The spatial distribution of snow water equivalent (SWE) is modelled as a two-parameter gamma distribution with parameters dependent on the number of accumulations and ablations.

The strict analytical control of the spatial distribution of SWE at all times allows for the development of algorithms which relates accumulated or ablated snow to changes in the snow-covered area (SCA) of a catchment. The algorithms are further developed so that remotely sensed information of SCA can be used to update the snow reservoir and the spatial distribution of SWE.

The snow distribution model and the updating algorithms are implemented in the Nordic HBV model and have been tested for ten Norwegian catchments. The overall improvements on the prediction of discharge by updating several satellite-derived SCA scenes are modest, but significant improvements for some scenes are observed (Figure 2.8). Errors and temporal inconsistencies in the quantification of SCA from the satellite scenes are found, which may lead to serious errors in the predicted discharge. The methodology is totally dependent on the quality of the SCA data and special care in quantifying SCA has to be taken for operational use of the updating algorithms.

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Figure 2.8 Successful updating for the Atnasjø catchment in 2002. Note how the snow reservoir in the top panel is sharply reduced in the middle of the melting period due to the assimilation of satellite-derived SCA.

Uncertainty in flood inundation models

Flood inundation models play a central role in both real-time flood forecasting and in floodplain mapping. In flood forecasting, inundation models should be as precise as possible to predict the approach of a flood correctly as well as to avoid false alarms. Flood mapping has to be accurate for a variety of reasons including decision-making for local planning or the insurance industry. A full understanding of the model and the uncertainty in the modelling strategy is therefore important.

Every flood inundation model will be an incomplete representation of reality as a result of multiple sources of uncertainty. We may distinguish the primary sources of uncertainty as follows:

• Choice of model structure as a simplification of reality (e.g. 1D or 2D flood inundation model or various representations of internal structures such as bridges)

• Numerical approximations in solution of equations defined in model structure

• Definition of boundary conditions, including input forcing data

• Choice of effective parameter values, including scaling and incommensurability effects.

Table 2.2 Flood events which have been studied within the FRIEND programme

Location Date Type of Data Publication

Usti nad Orlici (Czech Republic)

1997 Geometry, flood extent and 26 level observations

(Werner et al., 2005a) River Morava

(Czech Republic)

1997 Geometry, maximum level observations

(Pappenberger et al., 2005b)

Key findings

• Model parameters are effective parameters (Pappenberger et al., 2005a).

• Distributed observations of levels in floodplains have been shown to be most effective in constraining the uncertainty of flood inundation models (Werner et al., 2005a).

• Observations of flood extent in large events where flood extent is constrained by embankments and steep valley sides may not be suitable enough to discriminate between various model structures (Werner et al., 2005a).

• Sensitivity analysis of model performance against the calibration data shows that, as the number of land use classes increases, sensitivity to these roughness values decreases (Werner et al., 2005b).

• Sensitivity to the uncertainty to the upstream boundary depends on the model structure chosen (Pappenberger et al., 2005b; Pappenberger et al., in press).

• Internal structures such as bridges can have a profound effect on model performance (Pappenberger et al., in press).

• Under certain circumstances no parameter set or model implementation that fulfils all evaluation criteria can be established. We propose four different approaches to this problem: closer investigation of anomalies, introduction of local parameters, increasing the size of acceptable error bounds, and resorting to local model evaluation. Moreover, we show that it can be advantageous to decouple the classification into behavioural and

non-behavioural model data/parameter sets from the calculation of uncertainty bounds (Pappenberger and Beven, in press).

Uncertainty analysis of flood inundation models is essential to fully understand the limitations of the predictions and inundation models, and estimation of flood risk. However, there is no readily available guidance about how to do uncertainty analysis of flood inundation models.

Future research in uncertainty in flood inundation models will have to concentrate on this topic.

Flood frequency computation within the uncertainty framework

Continuous simulation on hourly time-steps is used for the flood frequency computation. First short (100 years) simulations are computed. From those, behavioural simulations are selected based on three goodness of fit criteria:

• sum of absolute errors between a Wakeby distribution fitted to modelled annual peaks for each realisation and the regional estimate. The errors are computed on the first four quantiles (1-, 2-, 5- and 10-year return periods) for which we expect the regionalised estimates to be most robust.

• sum of absolute errors between the regional flow duration curve and modelled curve on all the 13 quantiles available

• sum of absolute errors between Wakeby distributions fitted to maximum annual snow water equivalents observed and modelled on five quantiles (up to the 20-year return period estimate).

With the behavioural parameter sets long (10,000 years) simulations are performed and uncertainty bounds are computed (Blazkova and Beven, 2002).

In the conditioning on "observed" flood frequency curve only quantiles up to a 10-year return period are used. This is because observed data are only one realisation of the underlying process producing extremes. They do not necessarily go through the centre of the distribution of the possible realisations. For ungauged catchments regional estimates can be used for conditioning instead of observed data (Blazkova and Beven, 2002).

Predictions of peak flow are always uncertain and would be better given and disseminated not as a single value but as a cumulative distribution (Figure 2.9). Because of the large uncertainty in the estimates of extreme phenomena, the fuzzy set theory seems to be a good tool for model evaluation. The combination of several criteria is easily implemented and linguistic descriptions can also be used.

Spatial response of hydrological models: understanding runoff generation

For computing flood frequency on a large catchment a rainfall simulator which produces precipitation events moving across the catchment should be used. Moreover, such simulations should be conditioned also on discharge and snow information from the subcatchments (Blazkova and Beven, 2004, 2005). An additional criterion for excluding unbehavioural simulations can be the agreement of the results of the precipitation simulator with the Probable Maximum Precipitation.

In small catchments the investigation of spatial responses means finding out if the wetting of the catchment in the model agrees with reality. Various procedures can be used from the simple mapping of the saturated areas during wet and dry events on the catchment (e.g.

Figure 2.9 Predicted cumulative distributions of seasonal floods

Blazkova et al., 2002a) to the more sophisticated use of a large number of piezometers (Blazkova et al., 2002b). In the latter study about 50 piezometers were used in the Uhlirska catchment (1.87 km²) for one summer season (475 measurements altogether). Assuming hydrological similarity (all computing cells with the same value of the topographic index are hydrologically similar) prediction boundaries of water table depth have been estimated depending on the topographic index for a number of discharges.

Predictions of local water table levels with global catchment parameters gave results that were approximately correct but better reproduction of local water table responses might result from allowing local variations in the parameter values away from the global values. One of the most interesting issues is how far the local values reflect a real variation in soil properties, effective upslope contributing areas or other characteristics of the catchment, and how far they are compensating for deficiencies in the assumptions and structure of the model.

2.3.4 Catchment hydrological and biogeochemical processes in a changing